I think back up from the vet is important, but the only known mis-representation seems to be the age of the pup, however is there any proof about that, were you told the info (how do you prove a conversation) or was it in an advert or receipt when you bought her? Could she claim that you mis-heard her, after all a "few days" that she said off her 8th week could be 14 days as it isn't quantitfied.
TBH, I bought a horse some years ago who turned out to be going blind (cateracts), I didn't have her veted
prior to the sale and therefore was victim of the "buyer beware" situation and lost £1000+. The vet agreed that she'd probably got the condition at the time of sale but I couldn't claim a bean from anywhere as I had accepted her in good faith.
I don't want to put you off claiming but the last thing you need is another bill on top of the money you have lost.
A few days to check things out isn't going to make a huge difference and you could always put in writing a request to settle and say you are considering legal action or taking legal advice, then give her 14 days with the grounds for action. The court, if they agree there is a case, will then have extra evidence of the steps you took to settle the matter. Don't forget copies of all letters and diary of the calls whilst Charley was ill.